Galerkin method of smooth subdomain for efficiently analyzing structural stress
Galerkin method of smooth subdomain for efficiently analyzing structural stress
 CN 105,243,282 A
 Filed: 11/03/2015
 Published: 01/13/2016
 Est. Priority Date: 11/03/2015
 Status: Active Application
First Claim
1. a Galerkin method for the smooth subdomain of efficient analysis structural stress, it is characterized in that, the method comprises the following steps:
 the first step, and whole Problem Areas is divided into multiple subdomain, and in each subdomain, distribution is without the node of link information;
Second step, calculates each subdomain stiffness matrix and force vector;
3rd step, reduction subdomain degree of freedom;
4th step, obtains the overall discrete equation of reduction Problem Areas;
5th step, obtains the degree of freedom of all nodes of Problem Areas according to the degree of freedom on a node basis after reduction;
6th step, according to the shift value of all nodes in known Problem Areas, draws the structural stress of relative position.
Chinese PRB Reexamination
Abstract
The invention relates to a Galerkin method of a smooth subdomain for efficiently analyzing structural stress. The method comprises the following steps: (1) dividing an entire problem domain into a plurality of subdomains, and distributing nodes without link information in each subdomain; (2) calculating a stiffness matrix and a force vector of each subdomain; (3) reducing the freedom degree of each subdomain; (4) obtaining an overall discrete equation of the reduced problem domain; (5) obtaining the freedom degree of all nodes of the problem domain according to the reduced node freedom degree; and (6) obtaining the stress of a relative position according to displacement values of all nodes in the known problem domain. According to the Galerkin method, the technical problem of relatively long elapsed time in a meshless method calculation can be solved; and the problem of time consumption in a complex geometrical element division in an engineering problem is solved.
8 Claims

1. a Galerkin method for the smooth subdomain of efficient analysis structural stress, it is characterized in that, the method comprises the following steps:
 the first step, and whole Problem Areas is divided into multiple subdomain, and in each subdomain, distribution is without the node of link information;
Second step, calculates each subdomain stiffness matrix and force vector;
3rd step, reduction subdomain degree of freedom;
4th step, obtains the overall discrete equation of reduction Problem Areas;
5th step, obtains the degree of freedom of all nodes of Problem Areas according to the degree of freedom on a node basis after reduction;
6th step, according to the shift value of all nodes in known Problem Areas, draws the structural stress of relative position.
 the first step, and whole Problem Areas is divided into multiple subdomain, and in each subdomain, distribution is without the node of link information;

2. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 1, it is characterized in that, described second step is included in further in each subdomain and generates multiple smooth grids, adopt smooth strain gauge technique, the Line Integral of twodimensional problems is transformed into line integral, and obtains the stiffness matrix of each subdomain.

3. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 2, it is characterized in that, described second step comprises further:
 each smooth grid in traversal subdomain, and calculates the area of smooth grid;
Gauss integration point on traversal boundary segmentation;
Search the adjacent node of the whole node determination points in subdomain, calculate the corresponding stiffness matrix of described subdomain.
 each smooth grid in traversal subdomain, and calculates the area of smooth grid;

4. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 1, it is characterized in that, described 3rd step comprises further and is transformed on boundary node by transition matrix by the degree of freedom of internal node, and the degree of freedom of each subdomain is reduced.

5. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 1, it is characterized in that, described 3rd step comprises the method adopting static condensation further, by transition matrix, the degree of freedom of internal node is transformed on boundary node, the degree of freedom of each subdomain is reduced.

6. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 1, it is characterized in that, described 4th step comprises the stiffness matrix after the reduction calculating all subdomains further, stiffness matrix after reduction assembles by the mode according to finite element method, obtains the overall discrete equation reducing Problem Areas degree of freedom.

7. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 1, it is characterized in that, described step 5 comprises further, according to the degree of freedom on a node basis after the reduction calculated, obtain the degree of freedom of the internal node in each subdomain, i.e. the degree of freedom of all nodes in Problem Areas.

8. the Galerkin method of the smooth subdomain of a kind of efficient analysis structural stress according to claim 1, it is characterized in that, described step 6 comprises the shift value according to all nodes in known Problem Areas further, calculate the strain of any position in the displacement of any position in Problem Areas and Problem Areas, and then draw the structural stress of relative position.
Specification(s)